28 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES ENERGY-BASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION Anton N. Servetnik Centrl Institute of Avition Motors, Moscow, Russi servetnik@cim.ru Keywords: spin disk testing, burst speed, frcture criterion, strin energy density Abstrct FE modeling of burst speed tests of gs turbine engine (GTE) disks using stress-strin properties confirmed by tensile tests of specimen ws crried out. Stress strin stte (SSS) of disk during loding ws determined using the MSC. Softwre nd ANSYS commercil FE method softwre. Incrementl theory of plsticity with isotropic hrdening ws used to determine the distribution of plstic strins of disks during loding. It ws shown strong sensitivity of the burst speed to the choice of the yield function. Burst speed test results of vrious disk configurtions nd thermo-mechnicl lodings were compred with three-dimensionl elstic-plstic FEM nlysis results using energy-bsed frcture criteri. Nomenclture ij - strin tensor components pl - plstic strin ij - stress tensor components 1 - first principl stress 2 - second principl stress 3 - third principl stress - engineering circumferentil stress r - engineering rdil stress B - ultimte strength eqv - equivlent stress U - strin energy density U ver - verge strin energy density obtined t clcultions mde by verge vlues of mechnicl mteril properties U min - miniml strin energy density obtined t clcultions mde by minimum vlues of mechnicl mteril properties U * - criticl vlue of strin energy density U *ver - criticl vlue of strin energy density obtined t verge vlues of monotonic tensile tests U *min - criticl vlue of strin energy density obtined t miniml vlues of monotonic tensile tests n 100% - rotor speed t mximum engine regime n burst - burst speed reduced to n 100% n KB - burst mrgin ΔR - rdil elongtion of disk R, r - rdius r * - rdius of disk cylindricl section 1. Introduction In recent yers the GTE development nd certifiction efforts ctively hve been engging the clcultions which hve mde it possible to ssess lod-crrying cpbility of disk (burst speed) tht is mde from mteril hving the most unfvorble mechnicl properties insted of the experimentl disk strength vlidtion. Mny methods hve been developed to ssess the burst speed of disks. The limit equilibrium method is the trditionl method to ssess disk lod-crrying cpbility during designing [1]. This method is bsed on the ssumption tht frcture occurs over meridin or cylindricl disk sections (r = r * ) when: ( r) ( r), (1) B * * ( r ) ( r ). (2) r B The condition (1) mens tht circumferentil stresses re equl to ultimte strength of 1
ANTON SERVETNIK mteril in ll the points of meridin disk section. The condition (2) mens tht rdil stresses re equl to ultimte strength over cylindricl section t rdius r *. Criteri (1) nd (2) should be used simultneously. When determining the burst speed by this method, simple clcultive schemes re used tht don t tke into ccount influence of stress concentrtion, 3D SSS, effect of mting prts nd rel therml field of disk. The distinction between clcultive vlues nd experimentl dt comes to 20% in some cses. Use of FEM in clcultions mkes it possible to tke into ccount both structurl nd loding peculirities nd sttisticl sctter of mteril properties. While developing technique to ssess lod-crrying cpbility of disks, selection of mteril model nd frcture criterion is of gret importnce. Verifiction technique is required to be mde bsed on comprison of clcultive dt with experimentl ones. The developed criterion must be checked for nlysis of different disk designs mde from vrious lloys. In this work the energy-bsed frcture criterion ws selected s frcture criterion [2]. This criterion sttes tht frcture occurs t the instnt when strin energy density reches its criticl vlue U * in the most stressed disk point: U U *. (3) Strin energy density t point of rbitrry loded elstic-plstic body is defined by formul: U ijdij, i, j 1,2,3, (4) 0 Energy density vlue is the sum of two constituents U=U 0 +U f, where U 0 corresponds to strin energy density of volume chnge with no chnge in form nd U f corresponds to strin energy density of form chnge with no chnge in volume. In [3] nd [4] it ws shown strong sensitivity of the burst speed to choice of the yield function. Different yield surfces with the use of Hosford model [5] hve been investigted to find the best suited surfce shpe. In this work incrementl theory of plsticity with isotropic hrdening ws used to determine the distribution of plstic strins of disks during loding. Following the technique proposed, the clcultions hve been mde on two vition GTE disks (fig.1 nd fig.2). Fig.1. HPT disk 1. Drwing nd frgments of frctured disk (R in mm) Fig.2. Power turbine disk 2. Drwing nd sttic crck of disk (R in mm) The nickel powder lloy HPT disk 1 ws loded t norml temperture to the rottion rte n=0.96 n burst nd then stopped. Residul elongtions hve been mesured for vlidtion of mteril model prmeters. After tht disk 1 ws brought to burst. Metllogrphic method showed tht disk 2 originted its frcturing from the disk fir-tree slot bottom re. The power turbine disk 2 ws mde from new high-temperture forged Ni-bsed lloy; it ws loded t norml temperture up to the sttic mcro crck initition moment. Residul elongtions nd burst speed for experiment nd qusi-sttic solutions re compred. 2
ENERGY-BASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION 2. Tensile tests With use of frcture criterion (3) to mke clcultive ssessment of disk lod-crrying cpbility, the U * vlue is obtined t monotonic tensile tests (strin controlled conditions with stndrd strin rte ccording to ASTM E8/E8M-09 [6] nd ASTM E21-09 [7]). The tensile tests hve been crried out t Schenck test mchine (fig.3) which provides setting of mximum lod up to P=100kN. This test mchine contins precision frme, hightemperture clmps, hydrulic tooling. Specimen loding mode controlling nd strin monitoring were performed using extensometer (25 mm bse), instlled on working specimen prt. ) b) Fig.4.Definition of U * (-Ti bsed lloy, b-ni bsed lloy) 3.Identifiction of mteril model prmeters Fig.3. Schenck test mchines Tensile tests re crried out with getting full stress-strin curves up to ultimte stress followed by sttisticl processing of experimentl dt. The U * (T) vlue in ech test is defined s the re under stress-strin hrdening curve t the given test temperture. For exmple, fig.4 shows full stress-strin digrm nd definition of U * for Ti-bsed nd Ni-bsed lloys. Obviously, non-liner hrdening lw is necessry to use in mteril model. U *ver nd U *min re the sttisticl verge nd miniml vlues derived of experimentl dt (blck nd red lines respectively). During investigtion lod- crrying cpbility of turbo mchine disks physicl non-linerity should be tken into ccount. Physicl nonlinerity mens occurrence of significnt plstic strins in the process of loding (their vlue for mterils of ircrft GTE disks exceeds 5%). Incrementl theory of plsticity with isotropic hrdening ws used to determine the distribution of plstic strins of disk during loding. The equivlent strin is split into elstic nd plstic contributions. The increment of plstic strin is defined by the yield function: f d pl, (5) where λ 0. To define the best suited surfce shpe of the yield condition Hosford model is used in the yield function: f ( ) 0, (6) eqv 3
ANTON SERVETNIK 1/ 1 2 2 3 3 1 eqv. (7) 2 Yield loci 2 1 2 2 3 3 1 with severl vlues of is presented t fig.5. It is seen, tht v.mises criterion corresponds to =2 nd the close to Tresc criterion to. Also, prmeter llows to describe surfce between them. eqv Tble 1. Numericl nd experimentl residul deformtions of disk 1 in points 1 nd 2 (fig.1) Point 1 Point 2 Δ exp,% 0.78±0.04 * 1.27±0.04 * Δ fem,% (=2) 0.060-0.068 ** 0.070-0.076 ** Δ fem,% (=20) 0.46-0.55 ** 0.55-0.65 ** Δ fem,% (=80) 1.00-1.19 ** 1.18-1.37 ** * - mesurement error, ** - mteril properties scttering. The stress stte of web disk 1 is mostly bixil with high vlues of rdil nd circumferentil stresses nd limiting stte becomes rpidly in cse of Tresc criterion thn v.mises criterion. The clcultions provided with Tresc yield condition hd been found to be more relible thn v.mises condition nd used in clcultions of burst speed. Also, it cn be seen, tht we hd big scttering (20%) in mteril properties using proposed mteril elstic-plstic model. 4. Numericl simultion of burst speed Fig.5. Yield loci of Hosford model with severl vlues of A non-liner hrdening lw ( ) is obtined from full stress-strin digrm. The stress-strin curves of disk 1 lloy were obtined from tensile tests of 6 specimens cut out from disk work piece in circumferentil direction. The stress-strin curves of disk 2 lloy were obtined from tensile tests of 6 specimens cut out from disk work piece in circumferentil nd rdil directions. The ccurcy of prmeter hve been vlidted by comprison of numericl Δ exp =ΔR/R nd experimentl Δ fem residul deformtions of disk 1 in points 1 nd 2 (fig.1) nd presented in tble 1. Results with v.mises criterion (=2) underestimte experimentl results; results with close to Tresc criterion (=80) give good greement with experimentl residul elongtions. The technique is bsed on numericl simultion of spin tests using FEM wherein disk is brought to burst. Simultion is performed in elstic-plstic sttement specifying true stressstrin mteril curves nd step-by-step increse in disk speed (qusi-sttic) until frcture energy density U * reches its criticl vlue in most dmged disk point. Fig.6 nd fig.7 illustrte exmples of plotting finite-element grids for disks with detiled mesh in the zone of expected disk frcture. Fig.6. Finite-element grid of HPT disk 1 4
ENERGY-BASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION Fig.7. Finite-element grid of power turbine disk 2 Anlysis of results of SSS clcultions showed tht the most dmged point (node with mximum vlues of 1 nd i ) nd the crck originting re coincided in experiments. At step-by-step disk loding ll the components of strin nd stress tensors grow monotonously. Fig.8 illustrtes for disk 1 chnges of U ver nd U min depending on the unit disk speed n/n 100% clculted by verge nd the minimum vlues of mechnicl properties. Prediction of burst speed with v.mises criterion (=2) differ from experimentl burst speed on 5-6%; with close to Tresc criterion (=20...80) clcultion give ccurte prediction (less thn 1%) of burst speed. The trditionl method (1) gives inccurte prediction; the difference between clcultion nd experiment is 13%. The burst speed vlue for disk 2 using the proposed mteril model with =80 nd energy criterion differs from the experimentl dt by less thn 2% (fig.9). Fig. 9. Chnge of strin energy density in the most dmged disk 2 point 5. Conclusion Qusi-sttic FEM clcultions of residul deformtions nd burst speed of two GTE disks ws provided. For proposed elstic-plstic mteril model, Tresc yield condition hs been found to be more relible thn v.mises yield condition. The energy frcture criterion hs been proposed to be used to clculte lod-crrying cpbility of turbo mchine disks. Possibility of this energy frcture criterion ppliction hs been verified. The burst speed clcultions mde for disks of different configurtions nd mterils hve shown stisfctory fit (less thn 2%) to experimentl dt. The technique developed for numericl determintion of GTE disks burst speed will enble one not to crry out high-cost spin tests of disks. Numericl simultion involving the energy frcture criterion my be used to ssess the lod-crrying cpbility of disks tking into ccount the possible dverse combintion of mteril properties nd to optimize designs of rotors including the welded ones. Acknowledgement Fig. 8. Chnge of strin energy density in the most dmged disk 1 point The uthor cknowledge CIAM for permission to publish this work. 5
ANTON SERVETNIK References [1] Birger I.A., Shorr B.F., Demynushko I.V., Sizov R.N., Dulnev R.A., Thermo strength of mchine prts. // Moscow, Mshinostroenie, 1975, 454 p. [2] Krimbev K.D., Servetnik A.N. Numericl simultion of spin tests of turbo mchine disks. // Engine building Herld, Scientific-technicl journl, 2008, 3, p. 130 134. [3] M. Mziere, et l., 2009. Overspeed burst of elstoviscoplstic rotting disks: Prt I - Anlyticl nd numericl stbility nlysis. Europen Journl of Mechnics A/Solids 28 36-44. [4] M. Mziere, et l., 2009. Overspeed burst of elstoviscoplstic rotting disks: Prt II - Burst of superlloy turbine disk. Europen Journl of Mechnics A/Solids 28 428-432. [5] Hosford W., 1972. A generlized isotropic yield criterion. J. Appl. Mech. 39, 607-609. [6] Americn Society of Test nd Mterils ASTM E8/E8M-09: stndrd test methods for tension testing of metllic mterils, book of stndrds. [7] Americn Society of Test nd Mterils ASTM E21-09: stndrd test methods for elevted temperture tension tests of metllic mterils, book of stndrds. Copyright Sttement The uthors confirm tht they, nd/or their compny or orgniztion, hold copyright on ll of the originl mteril included in this pper. The uthors lso confirm tht they hve obtined permission, from the copyright holder of ny third prty mteril included in this pper, to publish it s prt of their pper. The uthors confirm tht they give permission, or hve obtined permission from the copyright holder of this pper, for the publiction nd distribution of this pper s prt of the ICAS2012 proceedings or s individul off-prints from the proceedings. 6